Water saturation modeling: an upscaling point of view

摘要

The paper addresses some mathematical aspects of water saturation modeling. The upscaling problem, i.e., the substitution of an equivalent homogeneous medium for the real heterogeneous one, is shown to have a simple solution. This solution ensures reproduction of observed effective saturation in wells, and suggests methods to distribute saturation between wells. Elements of common practice are shown to be questionable. In particular, attempts to correlate effective saturation with effective permeability may preclude reproduction of observed saturation, and may lead to significant errors between wells.